It's not either/or. A known error is a link to a problem. The problem exists until it is resolved._________________"Method goes far to prevent trouble in business: for it makes the task easy, hinders confusion, saves abundance of time, and instructs those that have business depending, both what to do and what to hope."
William Penn 1644-1718

Known Errors are documented in KEDB i.e Known Error Date Base and if it is a known Error then most of the times a solution is also there. If no work around for the error was found then it is not an error it is a problem, no matter if you the know the error or not. Error needs rectification while as problems need solution.

Going deep into terms like knowledge management and problem management in ITIL will surely help.
I hope my answer was help.
Any feedback is always welcomed

A known error is a problem for which you have a root cause and have a workaround Or a permenant fix. Generally there should be a Workaround as it is the one that is used by the Service desk to resolve issues. There may be few cases where you know the root cause . workaround and the permenant fix is not there and in that case there should be a Problem case logged. To sum up - YES if you know the root cause but the Workaround and fix is not known then you can log a Problem case for it. I have seen cases where people log problems for the root cause and fix known ... Remember that ITIL is just a framework